### Video Transcript

Comparing Fractions Using Models:
Same Numerator

In this video, we will learn how to
use models to compare proper fractions with the same numerator and explain how the
size of the denominator affects the size of the fraction.

Would you rather have two-thirds of
a doughnut or two-quarters of a doughnut? Both of these fractions have the
same numerator. The numerator is the number on the
top of a fraction. If you had two-thirds of this
doughnut, you would have two pieces. And if you had two-quarters, you
would also have two pieces. So maybe you think that having
two-thirds would be the same as having two-quarters. But when we’re thinking about the
size of a fraction, we need to look at the denominator. This is the number at the bottom of
the fraction.

The denominator tells us the size
of the fraction. If we’re thinking about thirds,
that means the whole amount has been divided into three equal parts. And when we think about quarters,
the whole amount has been divided into four equal parts. So when we compare two fractions
with the same numerator, we need to compare the denominators as well to tell us the
size of the fraction.

If we were to take our doughnut and
divide it into three equal parts, each part would be a third. And if we were to take our doughnut
and divide it into four equal parts, each part would be a quarter. By using these fraction strips, we
can see that one-third is bigger than one-quarter. So if one-third is greater than
one-quarter, two-thirds are greater than two-quarters. I would rather have two-thirds of a
doughnut than two-quarters because two-thirds is worth more. The bigger the denominator, the
smaller the part becomes.

We could also say that the smaller
the denominator, the bigger the part becomes. Would you rather have five-sevenths
or five twelfths of a hot dog? Again, both of these fractions have
the same numerator, but this doesn’t mean they have the same value. To work out the value of each
fraction, we need to look at the denominator. Five-sevenths is equal to five out
of seven equal parts. And five twelfths is equal to five
out of 12 equal parts. Which would give you the most hot
dog, five-sevenths or five twelfths?

Let’s model five-sevenths using a
fraction strip. The whole amount has been divided
into seven equal parts. Each part is worth one-seventh. Five of these parts have been
shaded blue to show five-sevenths. If we take the whole amount or a
fraction strip and divide it into 12 equal parts, each part is a twelfth. Five of these equal parts have been
shaded green to show five twelfths. If we compare our two models, we
can see that five-sevenths is worth more than five twelfths. The bigger the denominator, the
smaller the parts become. So I would rather have
five-sevenths of the hot dog.

So we’ve learned that when we
compare fractions with the same numerator, the size of the denominator affects the
size of the fraction. Let’s practice what we’ve learned
about fractions with the same numerator now by answering some questions.

Compare the fractions. Which symbol is missing? Four-fifths is equal to
four-sevenths, four-fifths is greater than four-sevenths, or four-fifths is less
than four-sevenths.

In this question, we have to
compare the two fractions we’ve been shown, four-fifths and four-sevenths. And we have to choose the correct
symbol to compare. Is four-fifths equal to
four-sevenths? We could think that these fractions
are equal because they both have the same numerator or the number on top of the
fraction, four-fifths and four-sevenths. Maybe you can already tell from our
fraction strips that these fractions are not equal. They’re both different sizes. So these fractions are not
equal. The missing symbol is not “equal
to.”

Is four-fifths greater than
four-sevenths? To find out, we need to compare the
denominator. If we take our whole amount or
fraction strip and divide it into five equal parts, each part is worth a fifth. And if we take our fraction strip
and divide it into seven equal parts, each part is worth a seventh. And we can see that one-fifth is
bigger than one-seventh. The more equal parts we divide the
whole amount into, the smaller the parts become. So the bigger the denominator, the
smaller the size of the fraction. So if one-fifth is greater than
one-seventh, four-fifths are greater than four-sevenths. The missing symbol is “greater
than.”

When we’re comparing two fractions
with the same numerator, the denominator tells us the size of the fraction. Four-fifths is greater than
four-sevenths.

Compare the fractions. Which symbol is missing? Three-quarters, three-eighths. Is the missing symbol equal to,
less than, or greater than?

In this question, we have to
compare the two fractions shown, three-quarters and three-eighths. And we have to select the correct
symbol to compare these fractions. Is three-quarters equal to
three-eighths? Both of these fractions do have the
same numerator, three-quarters and three-eighths. So you might be mistaken into
thinking these fractions are equal. But we need to look at the
denominator of each fraction because the denominator affects the size of the
fraction. And our two models help us to see
this.

If we take the whole amount and
split it into four equal parts, each part would be one-quarter. And if we take the whole amount and
split it into eight equal parts, each part is worth one-eighth. We can see that one-eighth is
smaller than a quarter. The more equal parts we divide our
whole into, the smaller each part becomes. So if one-eighth is less than
one-quarter, three-eighths is also less than three-quarters. Three-quarters is worth more than
three-eighths.

So the missing symbol is “greater
than.” Three-quarters is greater than
three-eighths. When we’re comparing two fractions
with the same numerator, we also need to compare the denominators because the size
of the denominator affects the size of the fraction. The missing symbol is “greater
than.”

What have we learned in this
video? We have learned how to use models
to compare fractions with the same numerator. We also learned that the size of
the denominator affects the size of the fraction.